Simplify; express your answer in exponential form. Assume $q\neq 0, p\neq 0$. $\dfrac{{(q^{2}p^{-5})^{-5}}}{{q^{4}p^{3}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(q^{2}p^{-5})^{-5} = (q^{2})^{-5}(p^{-5})^{-5}}$ On the left, we have ${q^{2}}$ to the exponent ${-5}$ . Now ${2 \times -5 = -10}$ , so ${(q^{2})^{-5} = q^{-10}}$ Apply the ideas above to simplify the equation. $\dfrac{{(q^{2}p^{-5})^{-5}}}{{q^{4}p^{3}}} = \dfrac{{q^{-10}p^{25}}}{{q^{4}p^{3}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{-10}p^{25}}}{{q^{4}p^{3}}} = \dfrac{{q^{-10}}}{{q^{4}}} \cdot \dfrac{{p^{25}}}{{p^{3}}} = q^{{-10} - {4}} \cdot p^{{25} - {3}} = q^{-14}p^{22}$